Tuned multifunctional magnetic nanoparticles for biomedicine

ABSTRACT

Magnetic nanoparticles and related devices and methods are described. Compositions and methods can include magnetic nanoparticles having a narrow size distribution for use in diagnostics and therapeutics.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional Patent Application No. 61/356,892, filed Jun. 21, 2010 entitled “TUNED MULTIFUNCTIONAL MAGNETIC NANOPROBES (TMN) FOR BIOMEDICINE,” and U.S. Provisional Patent Application No. 61/441,933, filed Feb. 11, 2011, entitled “SIZE-OPTIMIZED MAGNETITE NANOPARTICLES,” each of which are incorporated herein in their entirety by reference.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under grant numbers 0203069 and 0501421 awarded by the National Science Foundation and grant number R21 EB008192 awarded by the National Institutes of Health. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

The present invention relates to magnetic nanoparticles and related devices and methods. More specifically, the present invention relates to compositions and methods of making magnetic nanoparticles having a narrow size distribution for use in diagnostics and therapeutics.

Magnetic nanoparticles (also referred to as MNPs) are attractive agents for biomedicine due to strong intrinsic magnetism that, through interaction with a magnetic field, enables their detection or influence from deep within a living subject. Rightly, magnetic nanoparticles have been studied extensively as potential contrast agents or nanoparticle materials in molecular imaging applications based on magnetic resonance imaging (MRI), as well as carriers for magnetically assisted drug delivery and hyperthermia. Recently, a new imaging modality called magnetic particle imaging (MPI) was introduced as a technique for visualizing magnetic nanoparticles in humans and animals. MPI is fast, quantitative, sensitive, and features good spatial resolution, a combination that is difficult to realize in MR imaging of magnetic nanoparticles, because MPI directly probes the large magnetic nanoparticle moment rather than its indirect effect on proton relaxation, as does MR imaging. Noteworthy recent MPI studies include in vivo, real-time imaging of magnetic nanoparticles passing through a beating mouse heart and compact, single-sided scanners that can image a patient without first inserting them into a costly and potentially claustrophobic magnetic device.

Despite much exciting progress in MPI scanner design and related image processing, relatively little effort has been spent developing magnetic nanoparticles that optimize imaging sensitivity. In fact, for MPI to successfully move beyond proof-of-principle experiments into the clinic or preclinical research laboratory, it will be important to engineer magnetic nanoparticles that are optimized for MPI. Most recent studies have used commercially available magnetic nanoparticle agents, including Resovist® (Bayer Schering Pharma, Berlin) and Feridex I.V.® (AMAG Pharmaceuticals, Lexington, Mass.; trade name Endorem™ in Europe); these are far from being magnetically optimized for MPI and thus inhibit MPI from reaching its full potential in terms of both spatial resolution and mass sensitivity. For example, in Resovist®, which to date has been the most popular material for MPI studies, it has been shown that only 3% of the total sample mass contributes noticeably to the MPI signal. More efficient nanoparticles are desired for molecular imaging applications that depend on active targeting, where for the highest sensitivity, each unit of nanoparticle is desired to generate the maximum achievable MPI signal voltage. Furthermore, for quantitative imaging, the signal intensity, and therefore magnetic nanoparticle properties, are desired to be uniform and reproducible.

In addition, magnetic nanoparticles are an attractive option for site-specific cancer therapies because they can be remotely targeted by the application of external magnetic field gradients or other active and passive targeting methods. Once localized, Magnetic Fluid Hyperthermia (MFH), a therapeutic modality that utilizes alternating magnetic fields (AMF) to dissipate heat from the resulting relaxation losses in magnetic nanoparticles, can be used to induce localized heating. Heating cancer cells (typically to ˜42-43° C.) is known to disrupt cellular metabolism making adjuvant therapy by conventional established methods more efficient. A wide range of ferromagnetic nanoparticles can be synthesized for MFH. Due to their modest magnetic characteristics, however, magnetic nanoparticles need to be optimized in terms of their morphological (size, size distribution, shape), crystallographic (phase purity) and magnetic (relaxation) characteristics for effective application in MFH.

Unfortunately, current methods of making magnetic nanoparticles do not provide ample control over morphological (size, size distribution, shape), crystallographic (phase purity) and magnetic (relaxation) characteristics that can improve existing diagnostic and/or therapeutic techniques using magnetic nanoparticles. Thus, a need exists for improved magnetic nanoparticles suitable for use in various diagnostic and/or therapeutic techniques.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to magnetic nanoparticles and related devices and methods. More specifically, the present invention relates to compositions and methods of making magnetic nanoparticles having a narrow size distribution for use in diagnostics and therapeutics.

In one aspect, the present invention provides a composition of magnetic nanoparticles, comprising a population of magnetic nanoparticles having a narrow size distribution. In some embodiments, the present invention provides a composition of magnetic nanoparticles, comprising a population of magnetic nanoparticles having a narrow size distribution, wherein greater than about 70% of the magnetic nanoparticles in the population have a diameter that is less than 10.5 nanometers (nm) from the median diameter.

In another aspect, the present invention provides a method for making a composition of magnetic nanoparticles having a narrow size distribution. The method can include combining an iron precursor and a surfactant in an organic solvent. In some embodiments, the ratio of surfactant to iron precursor is greater than 10:1. The method can further include heating the iron precursor and the surfactant in the organic solvent to form a first population of magnetic nanoparticles, and combining the first population of magnetic nanoparticles with an amphiphilic polymer or molecule to form a second population of magnetic nanoparticles. The magnetic nanoparticles of the second population can include the amphiphilic polymer, have a narrow size distribution and can be dispersible in an aqueous solution.

In yet another aspect, the present invention provides a method for imaging magnetic nanoparticles. The method can include administering a population of magnetic nanoparticles to a subject, wherein the population of magnetic nanoparticles has a narrow size distribution, and exciting at least one magnetic nanoparticle in the population of magnetic nanoparticles with an imaging system.

In yet another aspect, the present invention provides a method of performing magnetic hyperthermia. The method can include administering a population of magnetic nanoparticles to a subject, wherein the population of magnetic nanoparticles has a narrow size distribution; and heating a cell in the vicinity of at least one of the magnetic nanoparticles in the population of magnetic nanoparticles.

In yet another aspect, the present invention provides a method of producing magnetic nanoparticles with a tuned size distribution for magnetic particle imaging. The method can include selecting a diameter of a magnetic nanoparticle that produces a maximum signal and/or maximum spatial resolution at a frequency used in magnetic particle imaging. The method can further include producing a population of magnetic nanoparticles having a median diameter of approximately the selected diameter of the magnetic nanoparticle that produces the maximum signal and/or maximum spatial resolution, wherein the population of the magnetic nanoparticles has a narrow size distribution.

For a fuller understanding of the nature and advantages of the present invention, reference should be had to the ensuing detailed description taken in conjunction with the accompanying drawings. The drawings represent embodiments of the present invention by way of illustration. The invention is capable of modification in various respects without departing from the invention. Accordingly, the drawings/figures and description of these embodiments are illustrative in nature, and not restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a method of making magnetic nanoparticles, in accordance with an embodiment of the present invention.

FIG. 2 shows an imaging system in accordance with an embodiment of the present invention.

FIG. 3 shows MPI signal testing results, in accordance with an embodiment of the present invention. Symbols represent nanoparticle samples. The error bars delineate the first standard deviation of the sample diameter distribution. The curves are simulated data for particles with the listed anisotropy constant from Equation 11 and a log normal distribution with standard deviation 0.1.

FIG. 4 is a schematic diagram of MPI transceiver coils, in accordance with an embodiment of the present invention. The central receive coil is wound with opposite sense from the two adjacent coils to inductively decouple the transmit and receive channels.

FIG. 5A shows MPI signal testing results, in accordance with an embodiment of the present invention. Symbols represent MNP samples, and the error bars delineate the first standard deviation of the sample diameter distribution. FIG. 5B shows simulated data for each experimental sample (in black) with measured points duplicated (in gray) for reference.

FIGS. 6A-C shows simulated MPI data for (A) different anisotropy constants K, (B) different diameter distribution widths (a), and (C) different driving field amplitudes H₀, in accordance with an embodiment of the present invention.

FIG. 7A-C shows (A) TEM image of ˜16 nm diameter magnetite nanoparticles; (B) magnetization curves for a range of particle diameters; and (C) magnetization curves before and after phase transfer for 12 nm MNPs and 5 months after phase transfer, in accordance with an embodiment of the present invention.

FIG. 8A-C shows (A) SLP of a range of MNP diameters; (B) heating capacity of MNPs coated with PMAO-PEG as measured in water and DMEM; (C) and DLS measurements of MNPs coated with PMAO-PEG, in accordance with an embodiment of the present invention.

FIG. 9 shows powder X-ray diffraction, θ-2θ scans, of magnetite nanoparticles, in accordance with an embodiment of the present invention. Sizes indicated in legends were determined by Scherrer's formula using the peak at 2θ=35.4°. The magnetite reference (bottom) was obtained from the International Centre for Diffraction Data (PDF#019-0629).

FIG. 10 shows (A) MNPs preferentially dispersed in the denser chloroform phase before phase transfer (left), while preferring the aqueous phase after phase transfer (right); (B) Zeta potential of MNP@PMAO-PEG as a function of pH; and (C) Hydrodynamic size measurements of MNP@PMAO-PEG in RPMI 1640+10% FBS cell culture medium as a function of time, in accordance with an embodiment of the present invention.

FIG. 11 provides in vitro cytotoxicity of MNP@PMAO-PEG in Jurkats. Viability measured via Luciferase assay and toxicity measured via LDH assay. MNPs were incubated for 24 hours in physiological conditions (37° C. and 5% CO₂), in accordance with an embodiment of the present invention.

FIG. 12 shows bright field images of Jurkat cells after 24 hours incubation with MNP@PMAO-PEG, in accordance with an embodiment of the present invention.

FIG. 13 shows specific loss power (W/g Fe₃O₄) as a function of size and size distribution (Frequency (f)=373 kHz and H₀=14 kA/m), in accordance with an embodiment of the present invention.

FIG. 14 shows in vitro heating of Jurkats using MNPs of diameters (A) 12 nm, (B) 13 nm and (C) 16 nm (AMF was applied for 15 minutes), in accordance with an embodiment of the present invention.

FIG. 15 shows cell viability relative to control calculated as AC OFF_(avg.)-AC ON_(avg.), in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to magnetic nanoparticles and related devices and methods. More specifically, the present invention relates to compositions and methods of making magnetic nanoparticles having a narrow size distribution for use in diagnostics and therapeutics.

I. Magnetic Nanoparticles Having a Narrow Size Distribution

The present invention provides a wide variety of magnetic nanoparticles that can be designed for several different types of applications, such as diagnostic and/or therapeutic purposes. For example, the magnetic nanoparticles of the present invention can include magnetic particles composed of a magnetic material, such as iron in oxidized form. In some embodiments, the magnetic nanoparticles can be composed of iron oxide. Magnetic nanoparticles can include, for example, magnetite (Fe₃O₄) and/or maghemite (Fe₂O₃) particles. In certain embodiments, the magnetic nanoparticles have a magnetite core that is a single, defect-free crystal of magnetite. The nanoparticles can have a variety of phases such as, e.g., a spinel phase. As described further herein, the magnetic nanoparticles can also include a magnetic core (e.g., a magnetite core) coated with amphiphilic molecules.

In one aspect, the present invention is based at least partially on fabrication of a population of magnetic nanoparticles having a size distribution that is surprisingly narrower than other previously reported magnetic particles. A population of magnetic nanoparticles having a narrow size distribution can provide a wide variety of advantages over existing magnetic particles. For example, magnetic properties can be highly dependent on the particle size, and in some cases, very small variations in size can exponentially improve or degrade the desired magnetic property. Producing magnetic nanoparticles with a narrow size distribution can influence magnetic imaging modalities (such as MPI or MRI) by selection and manufacture of a size that produces maximum signal and/or maximum resolution for improving imaging. Alternatively, localized tissue heating can be optimized by exciting narrowly sized magnetic nanoparticles that are located near, e.g., a cancer cell thereby improving options in magnetic hypothermia applications. These are just some of the improved capabilities provided by a narrow size distribution of magnetic nanoparticles. One of ordinary skill in the art will appreciate additional advantages in view of the present disclosure.

Thus, in one embodiment, the present invention provides a population of magnetic nanoparticles having a narrow size distribution. As provided herein, a “narrow size distribution” is intended to mean a distribution of magnetic nanoparticles that have sizes (e.g., diameters) that are within a certain specified range from a median diameter of the population of magnetic nanoparticles. The size distribution of magnetic nanoparticles can be determined by a variety of methods, and characterization of the distribution can depend on the method used to determine the sizes of the magnetic nanoparticles. Methods for analyzing sizes (e.g., diameters) of the magnetic nanoparticles include but are not limited to magnetic measurement techniques, optical techniques (e.g., photon correlation spectroscopy or dynamic light scattering) and imaging techniques (e.g., transmission electron microscopy).

The size distribution of a population of magnetic nanoparticles can be expressed in a variety of forms. For example, the size distribution can obey a log normal distribution, a normal distribution, a bimodal distribution, and the like. Various known techniques can be used to fit the size distribution a population of magnetic nanoparticles. In addition, the quality of fitting can be determined by a standard goodness of fit test, for example a chi-square test, or Kolmogorov-Smirnov test.

In some embodiments, sizes (e.g., diameters) in a population of magnetic nanoparticles can be characterized by a log normal distribution. In certain embodiments, the diameter distribution g(d) of magnetic nanoparticles can be approximated by a log normal distribution, as shown in Equation (1):

$\begin{matrix} {{g(d)} = {\frac{1}{\sigma \; d\sqrt{2\pi}}\exp \frac{{- \ln}\left( {d/d_{0}} \right)^{2}}{2\sigma^{2}}}} & (1) \end{matrix}$

where exp(σ) is the geometric standard deviation of the distribution and d₀ is the median diameter. For log normal distributions, standard deviation is not additive, but is multiplicative. Sigma (σ) can be described as the standard deviation of log(d), where d is the diameter and log(d) is distributed normally (i.e., defined by a Gaussian distribution). To determine a range of diameters for a population of magnetic nanoparticles, standard deviation for the distribution can be considered. For example, if sigma is 0.3, exp(σ) is 1.35 (unitless), then it can be interpreted that 68.3% of diameters in the distribution lie between d₀*exp(σ) and d₀/exp(σ) (unitless). In some embodiments, the population of magnetic nanoparticles will have a size (e.g., diameter) distribution that obeys a volume weighted (e.g., log normal) distribution function (e.g., as measured by magnetic measurement techniques or dynamic light scattering). In certain embodiments, the population of magnetic nanoparticles will have a size (e.g., diameter) distribution that obeys a number weighted (e.g., log normal) distribution function (e.g., as measured by transmission electron microscopy). The quality of fitting the log normal distributions can be identified by a standard goodness of fit test, for example a chi-square test.

In certain embodiments, the populations of magnetic nanoparticles that are described by log normal distributions can be described as having a median diameter and a standard deviation (σ), or alternatively exp(σ), which is the geometric standard deviation of the distribution (or a multiplicative standard deviation). Median diameters and diameter distributions can be determined, for example, using the Chantrell method, described in R. Chantrell et al., IEEE Trans. Magn. Mag. 14: 975-977 (1978). The median diameters of populations of magnetic nanoparticles of the present invention can range, for example, from about 10 nm to about 50 nm, from about 10 nanometers (nm) to about 30 nm, from about 10 nm to about 25 nm, from about 10 nm to about 20 nm, from about 15 nm to about 30 nm, from about 15 nm to about 25 nm, and from about 15 nm to about 20 nm. Multiplicative standard deviations (i.e., exp(σ)) for populations of magnetic nanoparticles of the present invention can be, for example, less than about 1.35, less than about 1.22, or less than about 1.11. Sigma (a) for these ranges corresponds to less than about 0.3, less than about 0.2, or less than about 0.1, respectively. In certain embodiments, the standard deviation (e.g., sigma) will decrease as the median diameter of magnetic nanoparticles is reduced.

The size distribution of a population of magnetic nanoparticles can also be expressed by a distance value from a median diameter of the population. For example, a percentage of magnetic nanoparticles can be characterized within nanometers distance from the median diameter of the population. For example, the narrow size distribution of magnetic nanoparticles can include a distribution where greater than about 70% of the magnetic nanoparticles in a population have a diameter less than 10.5 nm from the median diameter (e.g., as measured by a volume weighted log normal distribution function). In some embodiments, the narrow size distribution of magnetic nanoparticles can include a distribution where greater than about 70% of the magnetic nanoparticles in a population have a diameter less than 8.8 nm from the median diameter, as measured by a volume weighted log normal distribution function. In some embodiments, greater than about 70%, about 80%, about 90%, about 95% or about 99% of the magnetic nanoparticles in a population can have a diameter less than about 9 nm, about 8 nm, about 7 nm, about 6 nm, about 5 nm, about 4 nm, about 3 nm, about 2 nm or about 1 nm from the median diameter, for example, as measured by a volume-weighted (e.g., log normal) distribution function. In some embodiments, the narrow size distribution of magnetic nanoparticles can include a distribution where greater than about 70% of the magnetic nanoparticles in a population have a diameter less than 3 nm from the median diameter, as measured by a number weighted (e.g., log normal) distribution function. In some embodiments, greater than about 70%, about 80%, about 90%, about 95% or about 99% of the magnetic nanoparticles in a population can have a diameter less than about 5 nm, about 4 nm, about 3 nm, about 2.5 nm, about 2 nm, about 1.5 nm, about 1 nm, or about 0.5 nm from the median diameter, as measured by a number weighted log normal distribution function.

In addition to the nanoparticle core size characterizations described above, the populations of magnetic nanoparticles can also be characterized by hydrodynamic properties. For example, the populations of magnetic nanoparticles can include a mean hydrodynamic diameter, which, e.g., can be dependent on solution conditions and/or coatings of amphiphilic molecules on the surface of the magnetic nanoparticles. In certain embodiments, a population of magnetic nanoparticles of the present invention can include a mean hydrodynamic diameter ranging from about 20 nm to about 110 nm, from about 30 nm to about 100 nm, from about 40 to about 90 nm, from about 50 to about 80 nm, or from about 60 nm to about 70 nm in aqueous solution.

II. Methods of Making Magnetic Nanoparticles

The present invention includes methods of making magnetic nanoparticles described herein. A variety of techniques can be used that, for example, can depend on the desired size and/or properties of the magnetic nanoparticles. For example, the methods of making magnetic nanoparticles can be tailored to produce magnetic nanoparticles with sizes and magnetic properties that are optimal for particular diagnostic and/or therapeutic applications.

FIG. 1 shows a method 100 in accordance with an embodiment of the present invention. The method of making magnetic nanoparticles can include combining an iron precursor and a surfactant in an organic solvent (step 102), heating the iron precursor and the surfactant to form a first population of magnetic nanoparticles (step 104), and combining the first population of magnetic nanoparticles with additional amphiphilic small molecules or polymers to form a second population of magnetic nanoparticles (step 106).

In one example embodiment, the methods of the present invention include a method of making a population of magnetic nanoparticles that includes combining an iron precursor and a surfactant in an organic solvent to form an iron precursor solution. The ratio of surfactant to iron precursor can be, for example, greater than 10:1. The method further includes heating the iron precursor solution to form a first population of magnetic nanoparticles, and combining the first population of magnetic nanoparticles with an amphiphilic polymer to form a second population of magnetic nanoparticles that include the amphiphilic polymer. The second population of magnetic nanoparticles can have a narrow size distribution (e.g., a multiplicative standard deviation of less than about 1.35) and be dispersible in an aqueous solution.

As provided herein, iron precursor solutions of the present invention can include an iron precursor. A variety of iron precursor materials can be selected for making the magnetic nanoparticles. The iron precursor can include iron in a reduced or an oxidized (e.g., ferrous or ferric) state. In some embodiments, the iron precursor includes an iron ion (e.g., Fe³⁺) complexed with at least one other molecule. For example, the iron precursor can have the formula: Fe³⁺(R¹)₃, in which R¹ can include any compound capable of complexing with ferric iron to facilitate production of the magnetic nanoparticles. In one embodiment, the iron precursor has the formula: Fe³⁺(R¹)₃ wherein R¹ is a substituted or unsubstituted saturated C₁-C₂₄ carboxylic acid or a substituted or unsubstituted unsaturated C₁-C₂₄ carboxylic acid. In some embodiments, the iron precursor includes Fe³⁺-oleate or Fe³⁺-stearate

The iron precursor solutions used in making magnetic nanoparticles can further include a surfactant. The surfactant, for example, can be combined with the iron precursor for stabilization. A wide range of surfactants can be used. In some embodiments, the surfactant can include a substituted or unsubstituted C₁-C₂₄ alkane or a substituted or unsubstituted C₁-C₂₄ alkene. For example, the surfactant can include oleylamine. In certain embodiments, the surfactant can be a carboxylic acid. The carboxylic acid can be a substituted or unsubstituted saturated C₁-C₂₄ carboxylic acid or a substituted or unsubstituted unsaturated C₁-C₂₄ carboxylic acid. For example, the carboxylic acid can be oleic acid. Other types of surfactants, e.g., alkyl phosphines can be used. Alkylphosphine surfactants can include but are not limited to trioctylphosphane oxide (TOPO). In certain embodiments, the iron precursor can be combined with any combination of the surfactants described herein.

Substituents for the substituted compounds described herein (e.g., substituted C₁-C₂₄ alkane or a substituted C₁-C₂₄ alkene) can be one or more of a variety of groups selected from, but not limited to: —OR′, ═O, ═NR′, ═N—OR′, —NR′R″, —SR′, -halogen, —SiR′R″R′″, OC(O)R′, —C(O)R′, —CO₂R′, —CONR′R″, —OC(O)NR′R″, —NR″C(O)R′, —NR′—C(O)NR″R′″, —NR″C(O)₂R′, —NR—C(NR′R″R′″)═NR″″, —NR—C(NR′R″)═NR′″, —S(O)R′, —S(O)₂R′, —S(O)₂NR′R″, —NRSO₂R′, —CN and —NO₂ in a number ranging from zero to (2 m′+1), where m′ is the total number of carbon atoms in such radical. R′, R″, R′″ and R″″ each preferably independently refer to hydrogen, substituted or unsubstituted heteroalkyl, substituted or unsubstituted cycloalkyl, substituted or unsubstituted heterocycloalkyl, substituted or unsubstituted aryl (e.g., aryl substituted with 1-3 halogens), substituted or unsubstituted alkyl, alkoxy or thioalkoxy groups, or arylalkyl groups. When a compound disclosed herein includes more than one R group, for example, each of the R groups is independently selected as are each R′, R″, R′″ and R″″ groups when more than one of these groups is present. When R′ and R″ are attached to the same nitrogen atom, they can be combined with the nitrogen atom to form a 4-, 5-, 6-, or 7-membered ring. For example, —NR′R″ is meant to include, but not be limited to, 1-pyrrolidinyl and 4-morpholinyl. From the above discussion of substituents, one of skill in the art will understand that the term “alkyl” is meant to include groups including carbon atoms bound to groups other than hydrogen groups, such as haloalkyl (e.g., —CF₃ and —CH₂CF₃) and acyl (e.g., —C(O)CH₃, —C(O)CF₃, —C(O)CH₂OCH₃, and the like).

As provided herein, the present invention is based in-part on the discovery that the ratio of surfactant to iron precursor surprisingly can play a role in making magnetic nanoparticles with a narrow size distribution that can, for example, enhance magnetic properties and their uses. For example, lower molar ratios from 1:1 to 4:1 surfactant:iron precursor have been used to make magnetic particles. However, it was discovered that a large excess of surfactant as compared to iron precursor could be used to make magnetic nanoparticles. In particular, high ratios would have been expected to inhibit nucleation and particle growth. Surprisingly, high molar ratios of surfactant to iron precursor can be used to make populations of magnetic nanoparticles having narrow size distributions that have not been previously realized. The molar ratios of surfactant to iron precursor can range, for example, from greater than 5:1, greater than 10:1, greater than 15:1, greater than 20:1, and greater than 25:1. In some embodiments, the molar ratio of surfactant to iron precursor ranges from about 5:1 to about 40:1, from about 10:1 to about 40:1, from about 10:1 to about 30:1, and from about 10:1 to about 20:1. In certain embodiments, the molar ratio of surfactant to iron precursor is about 5:1, about 10:1, about 15:1, about 20:1, about 25:1, about 30:1, about 35:1 or about 40:1.

Organic solvents can also be included in the iron precursor solutions and other steps in the methods described herein. Organic solvents, for example, can be used in amounts that facilitate adjustment of the molar ratio of surfactant to iron precursor. The organic solvent includes a non-polar solvent. The selection of an organic solvent may under certain conditions depend on the surfactant and/or iron precursor being used. In some embodiments, the organic solvent includes a substituted or unsubstituted C₁-C₂₄ alkane or a substituted or unsubstituted C₁-C₂₄ alkene. In certain embodiments, the organic solvent includes octadecene. In some embodiments, the organic solvent can include oleylamine.

To allow for nucleation and particle growth at higher ratios of surfactant to iron precursor, certain steps can be taken during the methods of making magnetic nanoparticles. For example, solutions including iron precursor and surfactant can be heated under a given temperature and/or pressure for an extended period of time, e.g., longer than about 24 hours. In certain embodiments, nucleation of the magnetic nanoparticles can be delayed until after the iron precursor solution has been refluxed (e.g., heated) for between one to four hours, depending on the surfactant to iron precursor molar ratio. In certain embodiments, a higher ratio corresponds to longer times until nucleation begins. In addition, growth of the magnetic nanoparticles after nucleation can be longer than processes that involve low (e.g., 1:1) surfactant to iron precursor molar ratios. Depending on the high surfactant to iron precursor molar ratio used, the methods of making magnetic nanoparticles described herein can include heating processes longer than about 20 hours, longer than about 22 hours, longer than about 24 hours, and/or longer than about 26 hours.

Without being bound to any particular theory, it is believed that during the longer heating periods consistent with the present invention iron precursor concentration gradually reaches super-saturation due to gradual decomposition of the surfactant. For example, with methods including Fe³⁺-oleate as the iron precursor, the surfactant oleic acid can begin to dissociate from iron atoms at temperatures above 250° C. Heating at a temperature, for example, of 320° C. can cause gradual decomposition of the oleic acid thereby allowing for nucleation and then growth to occur. A longer period for growth, e.g., longer than 24 hours, may be due to a mechanism in which the acidic surfactant (e.g., oleic acid) partially dissolves the particles at the surface during the growth process, thus competing with ongoing growth and extending the growth time.

In certain embodiments, heating the iron precursor solutions described herein can include a variety of different heating phases. In some embodiments, heating the iron precursor solution can include a gradient temperature heating phase and a stable temperature heating phase. The order and duration of these phases can depend on the particular iron precursor, surfactant and/or organic solvent being used. For example, heating the iron precursor solution can include a gradient temperature heating phase followed by a stable temperature phase or vice versa. Rates of temperature increase during the gradient heating phase can be, for example, about 1° C./minute, about 2° C./minute, about 3° C./minute, 5° C./minute, about 10° C./minute, about 20° C./minute, about 30° C./minute, or about 40° C./minute. In an example embodiment using oleic acid, heating can include a gradient heating phase in which the iron precursor solution is heated to 320° C. at a rate of about 30° C./minute. Upon reaching 320° C., the solution can then be held at a stable temperature during a stable heating phase of longer than about 24 hours, or some other specified time (e.g., longer than 20 hours) that allows for production of the magnetic nanoparticles. In certain embodiments, the heating of the precursor solution can further include purging the solution under, for example, an argon and/or nitrogen atmosphere.

The surface properties of the magnetic nanoparticles provided herein can also be modified to effect solubility in non-polar and/or polar solvents. In certain embodiments, magnetic nanoparticles can undergo a phase transfer in which the surface of the magnetic nanoparticles is modified from a surface soluble in the non-polar organic solvent to a surface that is soluble in polar solvent, e.g., aqueous solution. For example, the methods of making magnetic nanoparticles can include forming a first population of magnetic nanoparticles that are not soluble (e.g., sparingly soluble) in aqueous solution. The first population of magnetic nanoparticles can be combined with an amphiphilic molecule, e.g., an amphiphilic polymer that modifies the surface of the magnetic nanoparticles, thereby making them dispersible in aqueous solution. The amphiphilic molecules or polymers can associate with the magnetic nanoparticles, for example, by covalent and/or non-covalent interactions with the surface of the magnetic nanoparticles. Moreover, surprisingly, the phase transfer process can actually cause a further narrowing on the size distribution for a population of magnetic nanoparticles. For example, a first population of magnetic nanoparticles produced in the iron precursor solution may have a broader size distribution than a second population of magnetic nanoparticles that is produced from a phase transfer process by, e.g., coating the magnetic nanoparticles with amphiphilic polymer.

A variety of amphiphilic molecules (e.g., polymers) can be used in the present invention. Suitable amphiphilic polymers include but are not limited to ethylene oxide/propylene oxide block copolymer, polyethylene oxide polymer, polyethylene glycol polymer, poly(maleic anhydride alt-1-octadecene) polymer and/or poly(maleic anhydride alt-1-octadecene)-polyethylene glycol polymer (PMAO-PEG). The amphiphilic polymers can have a wide range of molecular weights and can be linear or branched. In certain embodiments, the amphiphilic polymer can include Pluronic® F127. In some embodiments, the amphiphilic polymer can include PMAO-PEG. In one embodiment, the PMAO-PEG polymer can have a PMAO portion with a M_(n)˜30,000-50,000 and a PEG portion with a M_(n)˜5000. In some embodiments, the PMAO portion can range from about 1,000 to about 50,000, from about 5,000 to about 40,000, from about 10,000 to about 30,000, or from about 20,000 to about 50,000. Higher molecular weights can also be used. In some embodiments, the PEG portion can include, but is not limited to, PEG500, PEG1000, PEG2000, PEG5000, PEG10000, and higher.

III. Systems and Methods of Using Magnetic Nanoparticles

The magnetic nanoparticles of the present invention may find use in a wide variety of applications. For example, the present invention provides diagnostic and/or therapeutic methods of using magnetic nanoparticles described herein. In some embodiments, for example, the present invention provides methods for imaging magnetic nanoparticles that include administering a population of magnetic nanoparticles described herein to a subject and exciting at least one magnetic nanoparticle in the population of magnetic nanoparticles with an imaging system. The method can further include detecting a signal from at least one excited magnetic nanoparticle in the population of magnetic nanoparticles.

FIG. 2 illustrates various aspects of the present invention. For example, FIG. 2 illustrates a composition of magnetic nanoparticles 202 that can be delivered to a patient or subject prior to imaging. FIG. 2 also illustrates a basic configuration of an imaging system 200. The system 200 can, for example, include configurations/components commonly employed in known imaging systems. As shown, the imaging system 200 includes a patient or subject area 204 (positioned subject shown for illustrative purposes), a detector assembly 206 and a computer control unit 208. The computer control unit may include circuitry and software for data acquisition, image reconstruction and processing, data storage and retrieval, and manipulation and/or control of various components/aspects of the system. For certain applications, the detector assembly and subject area may be movable with respect to each other, and may include moving the detector assembly with respect to the subject area and/or moving the subject area with respect to the detector assembly. The components shown in FIG. 2 are provided for general illustrative purposes. One of ordinary skill will appreciate the modifications that would be associated with conducting different diagnostic (e.g., MPI and/or MRI) and/or therapeutic (e.g., MFH) techniques. For example, for MRI applications, the detector assembly 206 can be in the form of a conventional MRI scanner that houses the subject. Similarly, an assembly conventionally known for use with MPI can be arranged around the subject in place of the detector assembly 206.

A variety of imaging systems can be used to detect the magnetic nanoparticles in a subject, which can include but is not limited to an object, a plant, an animal, a mammal, or a human. In certain embodiments, the imaging systems can be configured to perform magnetic particle imaging (MPI) and/or magnetic resonance imaging (MRI). Commercially available and/or custom-built MPI and/or MRI systems can be used. MPI imaging can be carried out under a range of frequencies and amplitudes. In certain embodiments, the MPI imaging system can employ a frequency ranging between about 1 kHz to about 250 kHz, between about 1 kHz to about 100 kHz, and between about 1 kHz to about 25 kHz. Higher or lower frequencies can also be used.

The present invention also provides therapeutic methods that employ the magnetic particles described herein. In an example embodiment, the present invention provides a method of performing magnetic hyperthermia. The method includes administering a population of magnetic nanoparticles described herein to a subject and heating a cell in the vicinity of at least one of the magnetic nanoparticles in the population of magnetic nanoparticles. Heating of the magnetic nanoparticles can be accomplished using commercially available or custom built hyperthermia systems that, for example, can radiate the magnetic nanoparticles with an alternating magnetic field at a specified frequency and amplitude.

The present invention can further include selecting a particular magnetic nanoparticle size that is optimized for diagnostic and/or therapeutic applications described herein. For example, the present invention provides a method of producing magnetic nanoparticles with a tuned size distribution for magnetic particle imaging. The method can include selecting a diameter of a magnetic nanoparticle that produces a maximum signal at a frequency used in magnetic particle imaging and producing a population of magnetic nanoparticles having a median diameter approximately equal to the selected diameter of the magnetic nanoparticle that produces the maximum signal. The population of the magnetic nanoparticles can further have a narrow size distribution, as described above. In some embodiments, the present invention provides a method of producing magnetic nanoparticles with a tuned size distribution for magnetic particle imaging that can include selecting a diameter of a magnetic nanoparticle that produces a maximum spatial resolution at a frequency used in magnetic particle imaging and producing a population of magnetic nanoparticles having a median diameter approximately equal to the selected diameter of the magnetic nanoparticle that produces the narrowest spatial resolution. The population of the magnetic nanoparticles can further have a narrow size distribution, as described above.

Selecting a diameter of a magnetic nanoparticle that produces a maximum signal and/or a maximum spatial resolution can be performed through a variety of ways. For example, mathematical models can be used to simulate how a system of magnetic nanoparticles, with a selected diameter, will respond to an ac magnetic field to generate harmonics and therefore a signal recognized by, e.g., a magnetic particle imaging system. In one embodiment, the following model can be used: Magnetic nanoparticle susceptibility χ is modeled using the complex convention first developed to describe the permittivity of polar dielectrics in solution by Debye, such that

$\begin{matrix} {{\chi = {{\chi^{\prime} - {\chi}^{''}} = {\frac{\chi_{0}}{1 + ({\omega\tau})^{2}} - {\frac{\omega\tau}{1 + ({\omega\tau})^{2}}\chi_{0}}}}},} & (2) \end{matrix}$

where ω is the angular frequency of the applied magnetic field, τ is the time for the magnetic nanoparticle magnetic moment to reverse its direction, and χ₀ is the equilibrium susceptibility. For this approximation to be strictly valid, relaxation should be rotational and domain processes excluded and all particles should have identical size and shape.

Thus, for a driving field of the form

H(t)=H ₀ cos ωt=Re[H ₀ e ^(iωt)].  (3)

the magnetic nanoparticle magnetization is

M(t)=Re[χH ₀ e ^(iωt) ]=H ₀(χ′ cos ωt+χ″ sin ωt)  (4)

and M(t) contains both in-phase and out-of-phase terms due to the complex form of Eq. (2). The nonlinear equilibrium susceptibility χ₀ of superparamagnetic magnetic nanoparticles can be described by the Langevin function

such that

$\begin{matrix} {{\chi_{0} = {\frac{M\left( H_{0} \right)}{H_{0}} = {\frac{M_{s}}{H_{0}}{\mathcal{L}(\alpha)}}}},} & (5) \end{matrix}$

where

${\alpha = \frac{\mu_{0}H_{0}M_{s}\pi \; d^{3}}{6k_{b}T}},$

μ₀ is 4π×10⁻⁷ (Henry m⁻¹), H₀ is the equilibrium magnetic field strength in T μ₀ ⁻¹, k_(b) is the Boltzmann constant, 1.38×10⁻²³ (JK⁻¹), T is the temperature in Kelvin, and the magnetic moment of each particle is expressed in terms of the diameter d of its magnetic volume and volume saturation magnetization Ms in kA m⁻¹ (446 for bulk magnetite).

Magnetic nanoparticle susceptibility depends on the effective relaxation time τ for the magnetic nanoparticle moment to reverse in an alternating magnetic field

τ=τ_(B)τ_(N)/(τ_(B)+τ_(N)),  (6)

which includes two distinct relaxation processes, each with a characteristic time. For small-amplitude applied fields, the Neel relaxation time τ_(N) describes the magnetic reversal of an “unblocked” volume

$\begin{matrix} {{\tau_{N} = {\frac{\sqrt{\pi}}{2}\tau_{0}\frac{\exp \left\lbrack {K\; \rho} \right\rbrack}{\left( {K\; \rho} \right)^{1/2}}}},} & (7) \end{matrix}$

where K (Jm⁻³) is the magnetocrystalline anisotropy constant, a material property

${\rho = \frac{\pi \; d^{3}}{6k_{b}T}},$

and the attempt time τ₀ is ˜10⁻¹⁰ seconds. The Brownian relaxation time, τ_(B) describes the physical rotation of a “blocked” magnetic volume

$\begin{matrix} {{\tau_{B} = \frac{3{\eta\pi}\; d_{H}^{3}}{6k_{b}T}},} & (8) \end{matrix}$

where d_(H) is the magnetic nanoparticle hydrodynamic diameter and η (Pa sec) is the viscosity of the suspending fluid (0.89 for water). Equation (4) can also be modified to describe the magnetization M(t) of magnetic nanoparticles having a distribution of diameters g(d) in an alternating field of the form given in Equation 3, such that

$\begin{matrix} {{M(t)} = {{M_{s}{\int_{0}^{\infty}{\left( {{\frac{1}{1 + ({\omega\tau})^{2}}{\mathcal{L}\left( {\alpha \mspace{14mu} \cos \mspace{14mu} \omega \; t} \right)}} + {\frac{\omega\tau}{1 + ({\omega\tau})^{2}}{\mathcal{L}\left( {\alpha \mspace{14mu} \sin \mspace{14mu} \omega \; t} \right)}}} \right){g(d)}{{}.}}}}.}} & (9) \end{matrix}$

The diameter distribution g(d) is described above in Equation (1).

The present invention also provides methods and compositions for administering the magnetic nanoparticles described herein to a subject to facilitate diagnostic and/or therapeutic applications. In certain embodiments, the compositions can include a population of magnetic nanoparticles and a pharmaceutically acceptable excipient. Pharmaceutical excipients useful in the present invention include, but are not limited to, binders, fillers, disintegrants, lubricants, coatings, sweeteners, flavors and colors. One of skill in the art will recognize that other pharmaceutical excipients are useful in the present invention.

The magnetic nanoparticles of the present invention can be administered as frequently as necessary, including hourly, daily, weekly or monthly. The compounds utilized in the methods of the invention are administered at dosages ranging from, for example, about 1 mg to about 510 mg, or about 0.0125 mg/kg body weight to about 6.375 mg/kg body weight (assuming an average adult weighs 80 kg). The dosages, however, may be varied depending upon the requirements of the patient, the severity of the condition being treated and/or imaged, and/or the magnetic nanoparticle being employed. For example, dosages can be empirically determined considering the type and stage of disease diagnosed in a particular patient and/or the type of imaging modality being used in conjunction with the magnetic nanoparticles. The dose administered to a patient, in the context of the present invention should be sufficient to effect a beneficial diagnostic or therapeutic response in the patient. The size of the dose also will be determined by the existence, nature, and extent of any adverse side-effects that accompany the administration of a particular magnetic nanoparticle in a particular patient. Determination of the proper dosage for a particular situation is within the skill of the practitioner.

The compositions described herein can be administered to the patient in a variety of ways, including parenterally, intravenously, intradermally, intramuscularly, colonically, rectally or intraperitoneally. Preferably, the pharmaceutical compositions are administered parenterally, intravenously, intramuscularly or orally. The oral agents comprising a population of the magnetic nanoparticles of the invention can be in any suitable form for oral administration, such as liquid, tablets, capsules, or the like. The oral formulations can be further coated or treated to prevent or reduce dissolution in stomach.

The magnetic nanoparticle compositions of the present invention can be administered to a subject using any suitable methods known in the art. Suitable formulations for use in the present invention and methods of delivery are generally well known in the art. For example, a population of magnetic nanoparticles described herein can be formulated as pharmaceutical compositions with a pharmaceutically acceptable diluent, carrier or excipient. A population of magnetic nanoparticles of the present invention can be administered in any pharmaceutically acceptable composition. A pharmaceutically acceptable nontoxic composition is formed by incorporating any of normally employed excipients, and 10-95% of active ingredient or at a concentration of 25%-75%. Furthermore, in some embodiments, various carrier systems, such as nanoparticles, microparticles, or liposomes, etc. can be used. For example, magnetic nanoparticles can be encapsulated with other nanoparticles, e.g., liposomes. This approach can, for example, allow for a higher density of magnetic nanoparticles in an area, thereby influencing diagnostic and/or therapeutic applications. In addition, the magnetic nanoparticles can be further combined with drug delivery methodologies generally known in the art that, for example, employ nanoparticles for targeted drug delivery to a patient.

Furthermore, a population of magnetic nanoparticles can be formulated for parenteral, topical, nasal, sublingual, gavage, or local administration. For example, the pharmaceutical compositions are administered parenterally, e.g., intravenously, subcutaneously, intradermally, or intramuscularly, or intranasally. Thus, the invention provides compositions for parenteral administration that comprise a solution of a single or mixture of a population of magnetic nanoparticles described herein, dissolved or suspended in an acceptable carrier, preferably an aqueous carrier. A variety of aqueous carriers may be used. These compositions may be sterilized by conventional, well known sterilization techniques, or they may be sterile filtered. The resulting aqueous solutions may be packaged for use as is or lyophilized, the lyophilized preparation being combined with a sterile solution prior to administration. The compositions may contain pharmaceutically acceptable auxiliary substances as required to approximate physiological conditions including pH adjusting and buffering agents, tonicity adjusting agents, wetting agents and the like, such as, for example, sodium acetate, sodium lactate, sodium chloride, potassium chloride, calcium chloride, sorbitan monolaurate, triethanolamine oleate, etc.

The present invention also provides kits for administering the magnetic nanoparticles to a subject for treating and/or diagnosing a disease state. Such kits typically include two or more components useful for administration. Components can include magnetic nanoparticles of the present invention, reagents, containers and/or equipment. In some embodiments, a container within a kit may contain a magnetic nanoparticle composition including a radiopharmaceutical that is radiolabeled before use. The kits can further include any of the reaction components or buffers necessary for administering the magnetic nanoparticle compositions. Moreover, the magnetic nanoparticle compositions can be in lyophilized form and then reconstituted prior to administration.

In certain embodiments, the kits of the present invention can include packaging assemblies that can include one or more components. For example, a packaging assembly may include a container that houses at least one of the magnetic nanoparticle compositions as described herein. A separate container may include other excipients or agents that can be mixed with the magnetic nanoparticle compositions prior to administration to a patient. In some embodiments, a physician may select and match certain components and/or packaging assemblies depending on the particular diagnostic and/or therapeutic application.

The specific dimensions of any of the apparatuses, devices, systems, and components thereof, of the present invention can be readily varied depending upon the intended application, as will be apparent to those of skill in the art in view of the disclosure herein. Moreover, it is understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof may be suggested to persons skilled in the art and are included within the spirit and purview of this application and scope of the appended claims. Numerous different combinations of embodiments described herein are possible, and such combinations are considered part of the present invention. In addition, all features discussed in connection with any one embodiment herein can be readily adapted for use in other embodiments herein. The use of different terms or reference numerals for similar features in different embodiments does not necessarily imply differences other than those expressly set forth. Accordingly, the present invention is intended to be described solely by reference to the appended claims, and not limited to the preferred embodiments disclosed herein.

EXAMPLES Example 1

This example demonstrates a method of identifying an optimum size for magnetite nanoparticles that are used to generate MPI signal, where the signal is detected as the third harmonic of nanoparticle magnetization, M, for any driving field frequency, v. The experimental results, for an arbitrarily chosen v=250 kHz, agreed with predictions for a nanoparticle magnetization model based on the Langevin theory of superparamagnetism. By carefully controlling size, it is possible to engineer biocompatible magnetite nanoparticles with optimum physical dimensions that maximize MPI's mass sensitivity. This result is explained using the Langevin theory, is demonstrated experimentally, and provides a basis for synthesizing optimal materials with improved performance relative to commercial options.

Magnetite Nanoparticle Synthesis. Magnetite nanoparticles were synthesized by the pyrolysis of Iron (III) oleate in 1-Octadecene (technical grade, 90%, Aldrich). In a typical reaction to produce 15 nm magnetite nanoparticles, 12 mmol of oleic acid (technical grade, 90% Aldrich) was added to 0.5 mmol of the iron (III) oleate complex dissolved in 2.5 g of I-Octadecene. After purging under argon for 30 minutes, the mixture was heated, also under argon atmosphere, and refluxed for 24 hours. Finally, the reaction mixture was cooled to room temperature and the nanoparticles were collected and washed in a 1:1 mixture of chloroform and methanol.

To prepare for MPI signal testing, each sample was transferred from the organic to water phase for biocompatibility using the amphiphilic polymer, poly(maleic anhydride-alt-I-octadecene)-poly(ethylene glycol) (PMAO-PEG), and dissolved in 1× Phosphate Buffered Saline (PBS) solution. Following phase transfer, iron concentration was measured using an Inductively Coupled Plasma-Atomic Emission Spectrophotometer (Jarrel Ash 955). The iron concentration in synthesized samples generally ranged from 0.5 to 3.6 mg Fe/mL. The median diameter and size distribution of each was measured by fitting magnetization vs. field data according to the Chantrell method. (Chantrell et al., IEEE Transactions on Magnetics 1978; Mag-14(5): 975).

MPI Signal Testing. MPI signal performance was measured using a custom-built transceiver that was specially designed for detecting the 3rd harmonic of nanoparticle magnetization. During its operation sample harmonics are excited using an air-cooled solenoid that is driven at 250 kHz using a commercial radio-frequency (RF) amplifier (Hotek Technologies Model AG1OI7L). Harmonics are then detected using a smaller receiver coil and counter-windings that both reside coaxially inside. To narrow receiver bandwidth and provide optimal power transfer for harmonic detection, the receiver coil is tuned and matched to 50Ω at 750 kHz. Induced harmonics are also amplified using ˜24 dB of gain before detection with a commercial spectrum analyzer (Rohde & Schwarz, Model FSL303).

During testing, the transceiver transmitter coil was driven with 10 Watts of RF power to produce an excitation field of 10 mTμ₀ ⁻¹. To assess measurement variability, MPI signal testing was performed in triplicate. For each triplicate, 3 small cuvettes were filled with 100 μL of sample at the measured concentration listed in Table 1. Sample cuvettes were then inserted into the transceiver coils.

Langevin Model of Nanoparticle Magnetization. For a sample of nanoparticles, time dependent magnetization M, was modeled as a function of median nanoparticle diameter d₀ and standard deviation σ:

$\begin{matrix} {{\frac{M\left( {d_{0},\sigma,t} \right)}{M_{s}} = {\int_{0}^{\infty}{\left( {\frac{1}{1 + ({\omega\tau})^{2}} + {\frac{({\omega\tau})^{2}}{1 + ({\omega\tau})^{2}}}} \right)\left( {{{Coth}\left\lbrack {\alpha \; d^{3}{H\left( {\omega,t} \right)}} \right\rbrack} - \frac{1}{\alpha \; d^{3}{H\left( {\omega,t} \right)}}} \right){g\left( {d_{0},\sigma,d} \right)}{}}}},} & (10) \end{matrix}$

where H(ω,t) is the RF driving field, which varies sinusoidally with amplitude H and angular frequency

$\omega,{\alpha = \frac{\pi \; M_{s}\mu_{0}}{6k_{b}T}},$

where M_(s) is the saturation magnetization of the nanoparticles (446 kA/m for magnetite), μ₀ is 4π×10⁻⁷ Hm⁻¹, k_(b) is the Boltzmann constant, 1.38×10⁻²³ JK⁻¹, and T is the temperature in Kelvin; τ is the effective relaxation time for the particle moment to reverse in an alternating magnetic field, τ=τ_(B)τ_(N)/(τ_(B)+τ_(N)), where τ_(N) is the Neel relaxation,

$\begin{matrix} {{\tau_{N} = {\frac{\sqrt{\pi}}{2}\tau_{0}\frac{\exp \left\lbrack {K\; \rho} \right\rbrack}{K\; \rho^{1/2}}}},} & (11) \end{matrix}$

where K is the magnetocrystalline anisotropy constant,

${\rho = \frac{\pi \; d^{3}}{6k_{b}T}},$

and τ₀ is taken to be 10⁻¹⁰ sec, and τ_(B) is the Brownian relaxation,

${\tau_{B} = \frac{3V\; \eta}{k_{b}T}},$

where V is the hydrodynamic volume of the particle, and η is the viscosity of the suspending fluid (0.89 mPa s for water). Finally, g(d₀, σ,d) represents the distribution of diameters in the sample, and can be well-approximated using a log-normal distribution function:

$\begin{matrix} {{g\left( {d_{0},\sigma,d} \right)} = {\frac{1}{\sigma \; d\sqrt{2\pi}}\exp \frac{- \left( {\ln \left( {d/d_{0}} \right)} \right)^{2}}{2\sigma^{2}}}} & (12) \end{matrix}$

where σ is the standard deviation of the distribution, and d₀ is the median diameter.

By carefully controlling the size of the magnetic nanoparticles, it was demonstrated that MPI signal can vary dramatically with nanoparticle diameter, d. This is illustrated in FIG. 3 where measured signal per mg iron is seen to vary over nearly three orders of magnitude, with some particles exhibiting a 30 fold sensitivity increase over commercial counterparts with comparable iron concentration. There is an observed peak in the harmonic signal vs diameter, indicating that there is an optimum nanoparticle size for MPI at 250 kHz. This optimal size can depend on the drive frequency and the anisotropy constant K (Eq. 11), and can be predicted for other frequencies using the Langevin model discussed above. For 250 kHz MPI, the optimum particle diameter is ˜15 nm. Detailed information about the nanoparticle samples shown in FIG. 3 is provided in Table 1. Also included in FIG. 3, are three simulated curves, for Magnetite samples of increasing diameter, having anisotropy constants K of 15, 20, and 25 kJ/m̂3, respectively, each with a log-normal size distribution with standard deviation, σ=0.1.

TABLE 1 Details of Magnetite nanoparticle samples used in MPI signal testing. MPI signal mgFe/ D0 Sample (mV/mgFe) ml (nm) σ Feridex IV 10 2.21 6.9 0.40 (Bayer) mf090401 4 0.24 5.6 0.42 ak090309 <1 1.68 7.5 0.28 mf090806 72 0.68 12.4 0.18 mf090810p 136 1.56 14.0 0.12 mf090903p 168 2.72 14.3 0.17 mf090910p 310 1.10 15.0 0.22 mf090917p 221 3.64 15.8 0.09 mf090924p 204 3.12 16.3 0.07 mf091001p 88 1.73 17.0 n/a

Maximum signal was produced by sample mf090910p in Table 1. Size for sample mf091001p, which had an open loop at room temperature, was determined by TEM (FEI Tecnai G2 F20), and by the ratio of precursors relative to the other samples. The height and location of the peak in measured signal vs diameter (FIG. 3) quantitatively match the predicted values for magnetite nanoparticles with an anisotropy constant K of ˜20 kJ/m̂3. Measured values of K for magnetite typically ranged between 23-41 kJ/m̂3, while theory predicts 11 kJ/m̂3. The decrease in MPI signal for larger particles implies that, though the 10 mTμ₀ ⁻¹ excitation field is sufficiently large to generate harmonics, it is not large enough to shorten the effective relaxation time t, and instead relaxation is determined by particle size as discussed above. In fact, shortening should only occur at higher applied fields, H_(a), such that H_(a)>>H_(K), where H_(K)=2K/M_(s) the anisotropy field. The signal voltage per mg iron curve has a 9% average uncertainty, due to errors in the iron concentration and MPI signal voltage measurements.

Example 2

In this example, models described herein in Equations 1-9 above were used for simulations. Magnetite magnetic nanoparticles were synthesized by the pyrolysis of iron (III) oleate in 1-octadecene (technical grade, 90%, Aldrich). Iron (III) oleate was formed in a separate reaction, prior to nanoparticle formation, by dissolving 10 mmol of iron (III) chloride (anhydrous, Aldrich) in 50 ml methanol along with 30 mmol of oleic acid (technical grade, 90%, Aldrich). To this mixture was added, dropwise, 30 mmol of sodium hydroxide dissolved in 100 ml of methanol. The resulting waxy precipitate was washed five times with methanol, dried, dispersed in hexane, and washed five times with water in a separatory funnel. Finally, the product is dried again for storage and later use. In a typical reaction, to produce 15 nm magnetite nanoparticles, 12 mmol of oleic acid (technical grade, 90% Aldrich, St. Louis, Mo.) was added to 0.5 mmol of the iron (III) oleate complex dissolved in 2.5 g of 1-octadecene. After purging under argon for 30 min, the mixture was heated, also under argon atmosphere, and refluxed for 24 h. Finally, the reaction mixture was cooled to room temperature and the nanoparticles were collected and washed thoroughly in a 1:1 mixture of chloroform and methanol.

For phase transfer, a synthetic route was chosen based on organic solvents and surfactants because it leads to highly crystalline magnetic nanoparticles with narrow size distributions (typical σ of 0.1, corresponding to a 95% confidence interval of ±˜2 nm) and controllable size. However, since organic solvents are not suitable for use in biological imaging, the as-synthesized magnetic nanoparticles were transferred to the water phase. To ensure biocompatibility, organic residue was removed and the final magnetic nanoparticles were stable and not cytotoxic. The amphiphilic polymer poly(maleic anhydride-alt-1-octadecene)-poly(ethylene glycol) (PMAO-PEG) was used to affect phase transfer and dissolve the final magnetic nanoparticles in 1× phosphate buffered saline solution for testing.

For characterization, as-synthesized samples were dispersed on carbon TEM grids by a controlled evaporation of the solvent. Bright field images were then obtained using a FEI Tecnai TEM (Hillsboro, Oreg.) equipped with a Gatan CCD camera (Pleasanton, Calif.), operating at 200 KeV. Following phase transfer to aqueous solution, iron concentration was measured with an inductively coupled plasma-atomic emission spectrophotometer (Jarrel Ash 955). The iron concentration in synthesized samples ranged from 0.5 to 3.6 mgFe ml⁻¹. Magnetization vs field data M(H) was acquired with a LakeShore (Weterville, Ohio) vibrating sample magnetometer at room temperature. Sample UW170_(—)16 showed a slight open loop at room temperature and for this sample, M(H) data were acquired above the blocking temperature at 575 K using a Quantum Design (San Diego, Calif.) PPMS VSM oven. Saturation magnetization M_(s) (kA m⁻¹) was determined from M(H) data and the measured sample concentration by assuming density equal to stoichiometric magnetite (5180 kg m⁻³). The median diameter and diameter distribution of each sample were determined from M(H) data according to the Chantrell method.

MPI signal was measured using a custom-built narrowband transceiver designed to detect the third harmonic of magnetic nanoparticle magnetization. FIG. 4 shows a schematic diagram of transmit and receive coil arrangement in the MPI transceiver. During transceiver operation, an air-cooled, wirewound solenoid transmit coil excites sample harmonics that are then detected by a receiver coil. The transmit coil consists of 94 turns of 550 μm diameter copper wire and has a diameter and a length of 2.71 and 5.2 cm, respectively. The receiver coil is positioned inside the transmit coil and contains 140 total turns of 114 μm diameter copper wire. The receiver coil is designed to inductively isolate receive and transmit channels. It features three coaxial solenoids connected in series: Two outer coils each with 35 counterwound turns are positioned on either side of a central solenoid with 70 turns. The entire receiver coil has a diameter of 1 cm and a total length of 2 cm, with 3 mm spacing between the central and outer windings. During operation, the outer windings inductively decouple the receiver from the transmitter to reduce the level of harmonic noise that is detected. Additional use of radio-frequency (RF) traps and capacitive decoupling increases electrical isolation between the transmitter and receiver to well over 120 dB. The transmit coil was driven at 250 kHz by a commercial RF amplifier (Hotek Technologies, Tacoma, Wash., Model AG1017L). To narrow receiver bandwidth and provide optimal power transfer for harmonic detection, the receiver coil was tuned and matched to 50 at 750 kHz. Induced harmonics were also amplified using ˜24 dB of gain before detection with a commercial spectrum analyzer (Rohde & Schwarz, Munich, Germany, Model FSL303).

During testing, the transmitter coil was driven with 10 W of RF power to produce a sinusoidal excitation field with amplitude H₀˜6 mTμ₀ ⁻¹. To assess measurement variability, MPI signal testing was performed in triplicate. For each sample, three cuvettes were filled with 100 μl of sample at the measured concentration listed in Table 2. Sample cuvettes were then inserted into the transceiver coils and the signal was recorded. The normalized signal listed in Table 2 is the average of the three tested samples.

Numerical Simulations. MPI signal was simulated using MATHEMATICA software according to the models described herein. M(t) data were generated at a sampling rate of 4 MHz, sufficient to resolve the MPI signal at 750 kHz, by numerical integration of Eq. (2). The integration was limited to physically relevant diameters in order to reduce computing time. For each distribution, the integration bounds were chosen such that g(d) [Eq. (6)]>0.01 at the boundary d values. For all fields H₀ up to saturation, this condition yielded the same precision in M(t) to at least four significant figures, as setting the bounds from ˜0 to 1000 nm. The step size was chosen to ensure similar accuracy in M(t) at a range of fields up to saturation. The MPI signal was defined to be the emf induced in a receive coil by M3, the third harmonic of M(t), determined by discrete Fourier transform of M(t). According to the theory of reciprocity, this can be related to the axial field B_(axial) (TA⁻¹), produced by unit current in the receive coil

emf _(v)=6πf ₀ M _(s) B _(axial),  (10)

where f₀ is the driving field frequency.

MPI signal is plotted against the measured median diameter d₀ in FIG. 5A and characteristics of the measured MNP samples are provided in Table 2. All data have been normalized by iron concentration to allow comparison between samples. The signal voltage per mg iron has 12% average uncertainty due to errors in the iron concentration and MPI signal voltage measurements. The error bars are smaller than the dot size in FIG. 5A. Size-dependent signal generation can be seen in the figure, with a maximum value for sample UW150_(—)22 (median diameter equal to 15 nm).

TABLE 2 Properties of magnetite nanoparticles used in MPI signal testing. MPI signal mgFe/ M_(s) d₀ Sample (mV/mgFe) ml (kA/m) (nm) σ Feridex IV 10 2.21 223 6.9 0.40 UW056_42 3 0.24 225 5.6 0.42 UW075_28 1 1.68 155 7.5 0.28 UW124_18 72 0.68 322 12.4 0.18 UW140_12 136 1.56 384 14.0 0.12 UW143_17 163 2.72 203 14.3 0.17 UW150_22 291 1.17 347 15.0 0.22 UW158_09 233 3.45 293 15.8 0.09 UW163_07 216 2.94 300 16.3 0.07 UW170_16 91 1.66 309 17.0 0.16

FIG. 5B shows simulated data for each experimental sample. Normalized MPI signal voltage was calculated per mg iron, assuming stoichiometric magnetite of density 5180 kg m⁻³. Measured values of d₀, σ, and M_(s) were used as listed in Table 2; K was assumed to be the bulk value (11 kJ m⁻³), f₀ was 250 kHz, and H₀ was 6 mT μ₀ ⁻¹. Values of M_(s) listed in Table 2 have 20% average uncertainty due mainly to error in the sample volume used to measure M(H). The hydrodynamic diameter dH=d+2δ was used to determine the Brownian component of the effective relaxation time τ [Eq. (6)], where δ is the thickness of the polymer layer surrounding the magnetic core; in all simulations, δ was 10 nm, the length of the PMAO-PEG layer as measured by dynamic light scattering of MNPs before and after phase transfer.

FIG. 6 shows simulated data for magnetite MNPs to illustrate how changes in the anisotropy K, the standard deviation of the diameter distribution σ, and the driving field amplitude H₀ affect the signal voltage as a function of MNP size. In FIG. 6A, the range of K values is the expected range for magnetite nanoparticles, from the bulk value 11 kJ m⁻³ to a larger value 20 kJ m⁻³ that is in the middle of the range of values previously observed for particles smaller than 20 nm diameter.

By controlling MNP synthesis to produce a series of samples with closely spaced diameters and narrow size distributions, it has been demonstrated that MPI signal varies dramatically with MNP diameter, as predicted by models described herein. The observed normalized MPI signal is seen to vary over three orders of magnitude in the measured samples, with some particles exhibiting a 30-fold sensitivity increase over commercial counterparts with comparable iron concentration.

Our experimental device was designed to test the feasibility of generating harmonics for MPI imaging of small volumes, suitable for small animals. The driving field frequency, f₀=250 kHz throughout this work, was chosen accordingly. The field strength used in experiment (6 mTμ₀ ⁻¹) was chosen to limit coil heating, while the simulated fields in FIG. 6C were also chosen as relevant for imaging small animals at 250 kHz, where 12 mTμ₀ ⁻¹ is estimated to be the magnetic simulation threshold.

A feature of FIG. 5 is the observed peak in harmonic signal as a function of MNP diameter. This peak shows an optimum MNP size for MPI at 250 kHz. Comparing experimental data with the simulated data of FIG. 4B, we see quantitative agreement to within a factor of 2 for most samples. The exceptions include the two smallest samples, UW056_(—)42 and Feridex I.V.™, which also feature the largest a; sample UW143_(—)17, which has an unusually low measured Ms relative to its neighbors; and UW170_(—)16, the largest sample. Modeling samples UW056_(—)42 and Feridex was less reliable due to small median diameters and very broad distributions. Their measured distribution functions g(d) each include diameters as small as 1 nm, which is of the order of a single unit cell for magnetite.

In the simulated points of FIG. 5B, the signal voltage increases with diameter up to 15 nm, corresponding to the experimental data. However, a peak diameter is not clearly visible. In fact, given our assumption that K is equal to the bulk value (11 kJ m⁻³), samples up to at least 20 nm in diameter may be needed to clearly resolve the peak (shown in FIG. 5A). Experimental data showed a peak near 15 nm, from which may infer that the MNPs have anisotropy greater than 11 kJ m⁻³. For K=20 kJ m⁻³, the simulated data of FIG. 6A showed a peak at 15 nm. This is consistent with theoretical studies showing that nanoparticles can have an effective anisotropy greater than the bulk due to broken symmetry at their surfaces.

The same effects that yield increased K lead to a reduction in Ms with decreasing MNP size. This trend was observed in the samples: The average measured Ms is 70% (308 kA m⁻¹) of the bulk (446) value for magnetite for the samples with d₀ 10 nm; it is 45% (201) for samples with d₀<10 nm. The maximum concentration of 3.65 mgFe/ml (0.065 molFe/1) is quite low and it is unlikely that the small variations in sample concentrations contributed to the observed differences in MPI signal. The simulated results in FIGS. 6A-C provide insight into how the MPI signal strength will vary with sample properties and the driving field amplitude H₀. More generally, the model used herein and simulated results provide a physical understanding of the peak observed in the experiments. The decrease in MPI signal for MNPs larger than 15 nm in diameter is due to increased relaxation time τ. In small particles less than ˜10 nm in diameter, magnetic relaxation is dominated by the Neél process wherein the moment is thermally activated and typically reverses in nanoseconds. Brownian relaxation dominates in large particles greater than ˜20 nm in diameter. The moment of such particles is blocked or fixed along an easy axis, so that the entire particle physically rotates to align with an external field. The Brownian relaxation constant varies linearly with hydrodynamic volume and is substantially slower than Neél relaxation, its period ranging from microseconds to milliseconds depending on the thickness of the hydrodynamic layer that is made up of the surface coating(s) on the nanoparticles. Because the Neél relaxation time τ_(N) [Eq. (7)] depends exponentially on the magnetic volume, relaxation slows with increasing diameter in the region between 10 and 20 nm for magnetite. If the effective relaxation time τ is longer than the period of the driving field, one would expect the MNP moment to lag behind the driving field, the in-phase component of susceptibility to decrease, and the out-of-phase component to become more prominent. For the simulated data of FIGS. 6A-C, this transition corresponds to descent from the peak in MPI signal to the shoulder as the diameter increases. We note that the peak height varies with K, but the height of the shoulder, where relaxation is Brownian, does not. As expected, larger H₀ yield increased harmonic amplitude, especially for intermediate sizes where Néel relaxation dominates. The peak signal is seen to shift to slightly smaller diameters with increasing field.

The experimental data show that a detectable third harmonic can be produced by fields as small as 6 mT μ₀ ⁻¹. Furthermore, the measured decrease in MPI signal for larger sized MNPs implies that the 6 mT μ₀ ⁻¹ excitation field generated by our MPI transceiver during these experiments is not large enough to shorten the effective relaxation time τ. Therefore, the finite relaxation time should be considered as in Equations 1-9. We can estimate the field at which shortening is expected to occur; this should be when H_(a)>>H_(K), where H_(a) is the applied field and H_(K) is the anisotropy field. For bulk magnetite, which has cubic symmetry, H_(K)=4 K/(3 μ₀ M_(s))=34 mT μ₀ ⁻¹.

It has been shown with experiments that magnetite MNPs chosen for their optimized magnetic properties can show 30-fold improvement in normalized MPI signal over commercial samples, where the frequency of the driving field f₀ is 250 kHz and the MPI signal is measured at 3f₀. We have also observed a peak in MPI signal as a function of MNP size, with the diameter of ˜15 nm. A model of MNP magnetization based on the Langevin theory predicts a similar peak and gives some physical understanding of the underlying cause: The transition between Néel and Brownian relaxation results in a reduction in the MPI signal. Wherever the effective magnetic relaxation time τ of some samples under test approaches ½πf₀ in magnitude, there should be an optimum MNP size.

Example 3

In this example, it is shown that monodispersed MNPs (Fe₃O₄), synthesized in organic solvents and successfully transferred to water, can be tailored for strong size-dependent heating for any chosen combination of field frequency and amplitude. In order to establish biological relevance, heating rates were also measured in cell culture medium and the results interpreted in terms of changes in Brownian relaxation due to particle agglomeration.

Nanoparticles were synthesized according to a procedure based on pyrolysis of metal fatty acid salts; in this case, Fe³⁺-oleate. Fe³⁺-oleate was prepared and stored as a stock solution (conc. 18 wt. %) in 1-octadecene (ODE, technical grade 90%). Fe₃O₄ nanoparticles of desired sizes were synthesized by reacting predetermined amounts of Fe³⁺-oleate and oleic acid (tech. 90%) in ODE. For instance, synthesis of 15 nm particles used 0.2 mmol/g of Fe³⁺-oleate and 3 mmol/g of oleic acid in 2.5 g of reaction solvent (ODE). The mixture was refluxed overnight (˜24 h) at 320° C. under argon and vigorous stirring. The final product was collected and washed four times with a 1:1 (v/v) mixture of chloroform and methanol to remove excess surfactant and solvent. MNP powder, obtained by drying in vacuum for 30 min, was hydrophobic and easily dispersed in organic solvents such as toluene or chloroform. Phase transfer to aqueous phase was achieved by coating oleic acid coated MNPs (MNP@OA) with poly(maleic anhydride-alt-1-octadecene)-poly(ethylene glycol) (PMAO-PEG), an amphiphilic polymer. Colloidal stability of PMAO-PEG coated MNPs (MNP@PMAO-PEG) was characterized using Dynamic Light Scattering (DLS-Zetasizer Nano, Malvern Instruments). Iron concentration was determined using an inductively coupled plasma atomic emission spectrophotometer (ICP-AES, Jarrell Ash 955). A room temperature vibrating sample magnetometer (VSM, Lakeshore) was used to obtain magnetization results.

Heating rates of MNPs in water and tissue culture medium (Dulbecco's modified Eagle medium with 10% fetal bovine serum, DMEMb10% FBS) was measured using a dedicated hyperthermia system (magneTherm, nanoTherics, UK). Alternating magnetic field (AMF) frequency and amplitude were set at 376 kHz and 13.5 kA/m, respectively. A fiber optic thermocouple (Luxtron, Lumasense Technologies) was used to probe temperature. The power dissipation or SLP was measured using the following equation:

$\begin{matrix} {{S\; L\; {P\left( {{{watts}/{g{Fe}}_{3}}O_{4}} \right)}} = {c\frac{m_{{H_{2}O} + {{Fe}_{3}O_{4}}}}{m_{{Fe}_{3}O_{4}}}\left( \frac{T}{t} \right)}} & (13) \end{matrix}$

where c is the specific heat capacity of water (4.186 J/g ° C.), m_(Fe3O4) and M_(H2O+Fe3O4) are the mass of Fe₃O₄ MNPs and mass of whole sample in grams, respectively, and dT/dt is the temperature ramp rate in ° C./sec.

Transmission electron microscopy (TEM) imaging (FIG. 7A) shows that MNPs synthesized via the organic route are monodispersed (diameter of 16±1 nm is shown). For superparamagnetic particles, size and the lognormal size distributions were also determined by fitting magnetization curves to the Langevin function. Magnetization curves of MNP@PMAO-PEG in DI water for a range of sizes show increase in initial susceptibility and saturation with increasing particle size (FIG. 7B). Depending on the particle size, saturation magnetization values reach up to 80% of the bulk saturation value of magnetite, i.e., 90 emu/g. Due to spin disordering at the surface, saturation values of magnetite nanoparticles are often less than bulk values. Magnetization measurements before (MNP@OA) and after (MNP@PMAOPEG) phase transfer show negligible change in the magnetic properties (FIG. 7C). Finally, magnetic properties are consistent over the tested time period (5 months), suggesting excellent shelf life of MNP@PMAO-PEG.

Heating rates measured as a function of MNP size show a sharp peak in SLP at a diameter of 16 nm for σ_(avg)=0.175 (FIG. 8A). SLP values were calculated using equation (13). When particles of broader average size distribution (σ_(avg)=0.266) were used, the peak SLP value dropped from 144 to 100 W/g Fe₃O₄ (30% drop). These results confirm that a small increase in polydispersity can be negatively affect the heating capacity of MNPs.

In order to simulate biologically relevant environment, heating rates of MNPs dispersed in (DMEM with 10% FBS and 1% L-glutamine) were measured. FIG. 8B shows that MNPs of sizes 13 and 14 nm do not show any significant changes in SLP; however, 16 nm MNPs show a 30% decrease. DLS measurements FIG. 8C show that hydrodynamic size of MNP@PMAO-PEG increase when dispersed in DMEM+10% FBS. According to the magnetization relaxation theory of superparamagnetic nanoparticles, increase in hydrodynamic volume prolongs Brownian relaxation while the relaxation via Neel mechanism is unaffected. Furthermore, models show that, in water, 16 nm MNPs lie within the transition region from Neel to Brownian relaxation. Thus, based on our results, we infer that ˜30% of MNPs in the 16 nm sample were large enough to undergo Brownian relaxation and due to agglomeration in DMEM, the Brownian relaxation is blocked or too slow relative to the 376 kHz time window imposed by the AMF. The 13 and 14 nm samples did not show any significant change in SLP, even though they also agglomerated in DMEM (data not shown), suggesting primarily Neel relaxation. These measurements give significant insight into biological implications of hyperthermia. Even if MNPs are delivered in sufficient concentrations to target sites, adherence to cells and biomolecules is inevitable in in vivo situations and should be taken into consideration.

Example 4 Background

Since the idea of site-specific therapy is to restrict treatment to the cancer site, thereby minimizing side effects and patient discomfort, magnetic nanoparticles (MNPs) are an attractive option because they can be remotely targeted by application of external magnetic field gradients or other active and passive targeting methods. Once localized, Magnetic Fluid Hyperthermia (MFH), a therapeutic modality that utilizes alternating magnetic fields (AMF) to dissipate heat from the resulting relaxation losses in MNPs, can be used to induce localized heating. Heating cancer cells (typically to ˜42-43° C.) is known to disrupt cellular metabolism making adjuvant therapy by conventional established methods more efficient. A wide range of ferromagnetic nanoparticles, with superior magnetic properties, can be synthesized for MFH. However, iron oxide (γ-Fe₂O₃ or Fe₃O₄) magnetic nanoparticles show minimal toxicity and are FDA approved for MRI contrast agents and more recently for treatment of patients with chronic kidney disease. Furthermore, due to their modest magnetic characteristics when compared to the ferromagnetic elements, it is desired to optimize their morphological (size, size distribution, shape), crystallographic (phase purity) and magnetic (relaxation) characteristics for effective application in MFH.

MFH has been studied on both in vitro and in vivo platforms. However, the difficulty in delivering a sufficient amount of MNPs at the target site in order to promote a noticeable therapeutic outcome is one of the major hurdles impeding clinical adoption of MFH. For example, an estimated 32 mW of power dissipation for a treatment time of 10 minutes is used to raise the temperature of 1 g of prostate tumor tissue (cp ˜3.8 kJ kg⁻¹ s⁻¹) by 5° C. This is an underestimation and can be higher if cooling from blood perfusion is taken into account. Nevertheless, based on this rough estimate, a minimum dose of 0.32 mg of magnetic nanoparticles that have a Specific Loss Power (SLP) of 100 W/g, per gram of tumor tissue would be needed to locally raise the temperature by 5° C.

SLP output can be optimized if the effective magnetization relaxation time of MNPs match the applied AMF frequency. The effective relaxation time depends on both Neel (magnetization reversal) and Brownian (particle rotation) time components. Brownian relaxation (τ_(B)) depends linearly on the fluid viscosity (η) and the hydrodynamic particle volume (V_(H)), and is typically difficult to control due to the dynamic nature of the in vivo environment. It can also be detrimental to SLP output if the hydrodynamic volume is found to increase significantly. On the other hand, the operating Néel relaxation time (τ_(N)) depends exponentially on the product of magnetic anisotropy constant (K) and the magnetic core volume (V_(m)) τ_(N)˜exp (KV). Due to this exponential dependence, even slight increase in the size distribution alters the effective relaxation time. It is clear from the above discussion that the effective relaxation time, whether dominated by Néel or Brownian component, is dependent on the particle volume. Thus, it is desired to tailor particle size and, more importantly, the size distribution for a chosen AMF frequency, and also ensure MNPs do not agglomerate in biological medium in order to maximize SLP output. For instance, according to a model based on the known size-dependence of magnetic relaxation in MNPs, if size distribution increases from highly monodisperse (σ=0) to polydisperse (σ=0.25), heating rate degrades by a factor of 5. This changes the estimate above, which assumes ideally monodisperse MNPs, to ˜1.6 mg of polydisperse MNPs (σ=0.25) per gram of tumor tissue or 5 times more than needed.

Current MNP synthesis methods typically involve co-precipitation of iron salts in aqueous solution and lack the ability to produce monodisperse MNPs. So far, most studies of MFH utilize MNPs synthesized by such methods, and rely primarily on “extrinsic” augmentations in order to counteract the ineffectiveness of polydisperse MNP dispersions and improve therapeutic efficiency. Such augmentations include, directly injecting tumors with large quantities of MNPs or planting “thermoseeds” at tumor sites. However, in most cases the exact tumor location may be either unknown or require invasive methods to be reached. Increasing the administered MNP dose is also limited by the maximum tolerated dose (MTD); alternatively, increasing the applied magnetic field amplitude is also not an option as it can result in non-specific eddy current heating of surrounding tissue. Thus, an approach to optimize MFH is to intrinsically tailor the MNPs, which are the actual source of heating.

In order to tailor MNPs for optimized MFH response, highly monodisperse magnetite (Fe₃O₄) MNPs have been synthesized using organic methods and have been subsequently transferred to aqueous phase using a biocompatible amphiphilic polymer. The organic synthesis route gives control over size, size distribution, shape and phase purity, enabling synthesis of MNPs specifically tailored for any chosen AMF frequency. The resulting power output, or SLP, is maximum and optimized for that specific frequency. Systematic characterization was done to confirm that the synthesized MNPs possess the necessary characteristics for optimum MFH performance. A dedicated hyperthermia system was used to measure heating capacity of MNPs and identify the optimum size for our chosen AMF conditions (f=373 kHz, H₀=14 kA/m). Finally, the in vitro therapeutic effectiveness was compared for monodisperse MNPs to induce hyperthermia in cells as a function of concentration and size.

Materials and Methods

Chemicals Iron (III) Chloride, anhydrous (98%) was purchased from Alfa-Aesar. Oleic acid (tech. grade, 90%), 1-octadecene (tech. grade 90%), poly(maleic anhydride-alt-1-octadecene) (M_(n)=30,000-50,000), Pluronic®-F127 (M_(n)=12,600), methoxy poly(ethylene glycol) (M₀=5,000) and ethylene diamine were purchased from Sigma-Aldrich. 1-Ethyl-3-[3-dimethylaminopropyl]carbodiimide hydrochloride was purchased from Pierce Biotechnology. N-Succinimidyl 3-(2-pyridyldithio)propionate (99+%) was purchased from Molecular Biosciences.

Synthesis of Fe₃O₄ magnetic nanoparticles (MNPs). Magnetite MNPs were synthesized according to a procedure based on pyrolysis of metal fatty acid salts; specifically, Fe³⁺-oleate. Fe³⁺-oleate was prepared according to previous methods and stored as a stock solution (conc. 18 wt %) in 1-octadecene (ODE, technical grade 90%). A method was developed that allows reproducible synthesis of highly monodisperse Fe₃O₄ nanoparticles of diameters ranging from 10-25 nm by reacting pre-defined amounts of Fe³⁺-oleate and oleic acid (tech. 90%) in ODE. For instance, synthesis of 15 nm particles used 0.2 mmol/g of Fe³⁺-oleate and 3 mmol/g of oleic acid in 2.5 g of reaction solvent (ODE). The mixture was refluxed overnight (≧24 hours) at 320° C. under a blanket and vigorous stirring. Nucleation of nanoparticles was observed as a sudden change in color, from clear to black. The final product was collected and washed to remove excess surfactant and solvent. MNPs were precipitated using an excess of 1:1 (v/v) mixture of chloroform and methanol; they were then separated using a magnet and the washing step was repeated at least four times. MNP powder, obtained by drying in vacuum for 30 minutes, was coated with oleic acid and could be easily dispersed in organic solvents such as toluene or chloroform. X-ray diffraction (XRD-Rigaku) was used to confirm the crystalline phase of Fe₃O₄ and determine size of nanocrystals. A Vibrating Sample Magnetometer (VSM-Lakeshore) was used to measure magnetic properties of the samples.

Synthesis of PMAO-PEG. Methoxy-poly(ethylene glycol) (m-PEG, M_(n)=5,000) was used in the PEG-ylation of PMAO (M_(n)=30,000-50,000). PEG is considered highly biocompatible as it rejects non-specific protein adsorption, is non-immunogenic and non-toxic. Under acid catalysis, the hydroxyl group on m-PEG forms an ester bond with the anhydride ring on PMAO. In a typical reaction 2 g of PMAO (˜50 μmol) was reacted with 3.75 g of m-PEG (750 μmol) in 20 ml of acetone. A few drops of concentrated sulfuric acid were added to catalyze the reaction. The mixture was refluxed at 58° C. in an argon atmosphere. After 24 hours, the mixture was cooled to room temperature and the polymer was obtained by precipitation in excess DI water. After several more DI water washes by sonication and centrifugation, the white polymer cake was freeze dried for 24 hours. The final product was obtained as a white powder and stored at room temperature. Gel Permeation Chromatography (GPC) was used to confirm the increase in molecular weight after PEG-ylation (data not shown).

Phase transfer of hydrophobic MNP using PMAO-PEG. In a typical phase transfer process, about 10 mg of oleic acid coated MNP (MNP@OA) and 10 mg of PMAO-PEG were dissolved in 1-2 ml of chloroform. The mixture was sonicated in an ultrasonic bath for about 15 minutes and dried under a stream of argon. The dried nanoparticle-polymer complex was dispersed in 1 ml of 1× Tris-acetate-EDTA (TAE) buffer by a 30-minute sonication step. MNP coated PMAO-PEG (MNP@PMAO-PEG) were filtered using a 0.45 μm nylon syringe filter. In order to remove excess unbound polymer, MNP@PMAO-PEG were passed through a Sephacryl™ S-200 HR gel column (GE Healthcare Life Sciences). Either de-ionized (DI) water or 1× phosphate buffered saline (PBS) was used as the eluent. Nanoparticles were stored at 4° C. until further use. Iron concentration was determined using an Inductively Couple Plasma Atomic Emission Spectrophotometer (ICP-AES, Jarrell Ash 955)

Colloidal stability measurements. In order to understand the colloidal properties of MNP@PMAO-PEG, zeta potential and hydrodynamic size measurements were done using dynamic light scattering (DLS) technique (Zetasizer Nano, Malvern Instruments). For biological relevance, hydrodynamic size measurements were also made in cell culture medium.

Cytotoxicity study. Jurkat cells (human T-cell leukemia cell line) were grown in RPMI 1640 medium+10% fetal bovine serum (FBS) in physiological conditions (37° C. and 5% CO₂). Complementary assays were conducted to confirm there is reasonable correlation between cell viability and induced toxicity. A Lactate Dehydrogenase (LDH) assay (Cytotox-ONE®, Promega) was used to determine MNP toxicity to cells by measuring LDH release in medium due to membrane disintegration. Cell viability was determined using a luciferase assay (Celltiter-GLO®, Promega), which measures ATP levels. Cells were seeded at 20,000 cells/well in a 96-well plate. MNP concentrations of 150 μgFe/ml, 300 μgFe/ml and 450 μgFe/ml were tested for 24 hours in physiological conditions. Appropriate controls were included to ensure assay validity and test for any interference MNPs or media may have with the assay. A microplate reader was used to measure fluorescence at λ_(ex)=560 nm and λ_(em)=590 nm for LDH assay, and a luminometer (TopCount, Perkin-Elmer) was used for measuring luminescence in the luciferase assay.

In vitro hyperthermia. An alternating magnetic field (AMF) of frequency, f=373 kHz, and amplitude, H₀=14 kA/m, was generated using a dedicated commercial hyperthermia system (MagneTherm™, NanoTherics Limited, UK). Jurkat cells were cultured in triplicates at a density of 10,000 cells/well. MNPs of three sizes (12, 13 and 16 nm) with varying concentrations were added to the cultured cells. Prior to AMF heating, samples and controls were incubated at 37° C. for 15 minutes to stabilize temperature. Samples were enclosed in a thermally insulating Styrofoam™ jacket before inserting in the instrument's coil assembly. After 15 minutes of AMF application, samples were returned to the 37° C. incubator. Cell viabilities were compared using the Celltiter-GLO® luciferase assay.

Results

Characterization of Fe₃O₄ MNPs. Synthesized MNPs were highly monodisperse as characterized by TEM imaging. Hydrodynamic size of MNPs, before and after coating with PMAO-PEG, was measured using Dynamic Light Scattering (DLS). Magnetization curves, M(H), from VSM measurements were fit to the Langevin function, to obtain median magnetic core size and the volume-weighted size-distribution, using the Chantrell method. Average diameters and corresponding standard deviations, assuming a lognormal distribution, are shown in Table 3. Magnetic properties were reconfirmed after organic to aqueous phase transfer; example of a 12 nm sample, before, after and 5 months after coating.

TABLE 3 Median diameters and standard deviations of as-synthesized MNPs, derived from Chantrell fitting of magnetization curves. Size (nm) Std. Dev. (σ) 12 0.01 13 0.1 14 0.21 15 0.23 16 0.16 18 0.34

Powder X-ray diffraction θ-2θ scans of as synthesized MNPs are shown in FIG. 9. The scans show a good match with the powder diffraction file (PDF) for magnetite (#019-0629, International Centre for Diffraction Data). As indicated in the figure, scans for MNPs of two sizes are included (top and middle). Since smaller particles (<15 nm) are nearly spherical in shape (TEM data not shown), a modified version of Scherrer's formula accounting for the spherical geometry was used to determine crystal size of smaller particles (top spectrum). The generalized form was used for larger MNPs (middle scan) due to their noticeable non-spherical geometry characterized by faceting. The peak at 35.42° (θ=17.71°) was chosen for all crystallite size calculations. The calculated crystal sizes are 13.7 nm and 16.9 nm for the top and middle scans, respectively. These are in good agreement with the corresponding magnetic diameters determined by the Chantrell fitting method, which are 12.9 nm and 15.9 nm, respectively.

Colloidal stability. MNPs preferentially disperse in the aqueous phase after coating with PMAO-PEG (FIG. 10(A)) and show no signs of physical agglomeration or aggregate formation for several months. Long-term colloidal stability of MNPs in water was determined by measuring zeta potential as a function of pH (FIG. 10(B)). MNPs display a neutral surface charge across a wide range of pH values (2-12). Additionally, for biological relevance, hydrodynamic size measurements were also done in cell culture medium (RPMI 1640+10% FBS) to ensure MNPs remain stable during in vitro experiments (FIG. 10(C)). MNPs show no significant change in hydrodynamic size up to a period of 96 hours of incubation in RPMI 1640 medium.

Cytotoxicity. FIG. 11 shows results of MNP@PMAO-PEG cytotoxicity in Jurkat cells. Complementary viability (Luciferase assay) and toxicity (LDH release assay) studies were done to confirm validity of the performed assays. Cell viability drops to about 75% for the lowest concentration tested (150 μgFe/ml), while similar levels, within the calculated errors, are maintained for higher concentrations (300 and 450 μgFe/ml). The trend observed in the toxicity measurement agrees reasonably well with that observed in the viability measurement. Additionally, bright field images of cells incubated with MNPs were captured to examine any subsequent morphological alterations (FIG. 12A-H). Jurkat cells are suspension cells and do not adhere to culture plates, as indicated by their spherical shape (FIG. 12 (A&E)). The cellular structure and shape is consistent with the control (no MNPs) for all concentrations of MNPs (FIG. 12 (B-D) & (F-H)).

Magnetic Fluid Hyperthermia. MNPs of various sizes (Table 3) were tested for specific loss power (SLP, watts/g) in a dedicated hyperthermia system. The AMF frequency and amplitude were set at 373 kHz and 14 kA/m respectively. A fiber-optic thermocouple (Luxtron, Lumasense Technologies) was used to measure the temperature ramp rate (dT/dt) in samples. SLP was measured using the following equation:

$\begin{matrix} {{S\; L\; {P\left( {{{watts}/{g{Fe}}_{3}}O_{4}} \right)}} = {c\frac{{mass}_{Sample}}{{mass}_{{Fe}_{3}O_{4}}}\left( \frac{T}{t} \right)}} & (14) \end{matrix}$

where c is the specific heat capacity of water (4.187 J g⁻¹° C.⁻¹). Two sets of samples with average standard deviations (σ) of 0.175 and 0.266 were measured to specifically characterize effects of both size and size distribution on the power output. Such characterization is intended to emphasize the significance of tailoring size to a specific frequency, thus intrinsically optimizing MFH from a material perspective rather than augmenting extrinsic factors such as concentration or field amplitude. FIG. 13 shows a distinct peak in SLP at 16 nm for MNPs with narrow average size distribution. SLP values drop by ˜30% for samples with broader average size distribution. The drop is especially substantial for 16 nm particles, the peak diameter for a 373 kHz field.

In vitro hyperthermia. In order to study the in vitro effect of magnetic fluid hyperthermia, ATP levels in Jurkat cells, as a measure of metabolic activity or cell viability, were compared. In general, cells experiencing MFH showed a decrease in viability compared to controls (no MFH). This trend was consistent with increasing MNP concentration (FIG. 14). Monodisperse MNPs of three different diameters were compared. 16 nm MNPs, the optimal size for our chosen AMF as per the SLP data (FIG. 13), were compared with 12 and 13 nm MNPs. The decrease in viability is markedly greater for the 16 nm MNPs compared to 12 and 13 nm MNPs (FIG. 15). Also note, MNP concentration is slightly lower for 16 nm sample compared to 12 and 13 nm samples.

Discussion

TEM and analysis showed that the Fe₃O₄ MNPs were highly monodisperse and single phase, respectively. Additionally, magnetic properties of MNPs are superior, with saturation magnetization reaching as high as 75 emu/g for 16 nm MNPs (i.e. ˜83% of bulk saturation value for magnetite (˜90 emu/g). Due to the presence of ˜0.5 nm layer of disordered spins on the surface of the MNPs that do not contribute to the total saturation magnetization of the sample, superparamagnetic particles often have lower saturation values compared to bulk. It also explains why the crystalline diameter, determined from XRD spectrum, is ˜1 nm larger than the magnetic core diameter, determined by the Chantrell method. After transfer from organic to aqueous phase using the amphiphilic PMAO-PEG polymer, MNPs show exceptional stability in water (e.g., up to a year) and retain their superior magnetic properties up to a tested period of 5 months. The magnetic core diameters as determined using the Chantrell method confirm MNPs remain nearly monodisperse even after phase transfer (Table 3), suggesting no aggregation during the phase transfer process. Zeta potential as a function of pH shows MNPs display a near neutral surface charge across a wide pH range (2-12). This suggests MNPs are primarily stabilized via steric repulsion due to the surface PEG layer, and are less prone to adsorption form charged proteins or, in general, non-immunogenic. Hydrodynamic size measurements performed in cell culture medium (FIG. 10C) emphasize the biological relevance. For particles agglomerating in culture medium, the Brownian component of the relaxation, which depends on the hydrodynamic volume, can be blocked, decreasing the overall SLP output. MNP@PMAO-PEG are relatively stable for up to 96 hours in RPMI 1640+10% FBS cell culture medium, suggesting consequent decrease in SLP output due to particle agglomeration is not expected.

Cytotoxicity results confirm MNPs exhibit relatively low inherent toxicity in Jurkat cells (FIG. 11). Typically, the total amount of iron stores in the human body is approximately 3500 mg and the total amount of iron oxide used for diagnostic imaging is relatively small (˜5.6 μgFe/ml). The maximum concentration used in our cytotoxicity experiments (up to 450 μgFe/ml) is far greater than the actual in vivo use. This ensures that we are measuring for cytotoxicity beyond current clinically tried levels. Overall, both viability and toxicity assays complement each other reasonably well, within the calculated error. Bright field images of cells (FIG. 12) at 20× and 60× magnification confirm that overall cell morphology is preserved after 24 hours of incubation with MNPs of various concentrations.

Comprehensive experimental SLP data as a function of both size and size distribution (FIG. 13) shows that, for the chosen AMF conditions (373 kHz and 14 kA/m), 16 nm monodisperse MNPs exhibit the optimum SLP. More importantly, a clear peak in the heating as a function of MNP size is demonstrated for the first time. Additionally, MNPs with broader average size distributions show an overall drop in the peak SLP value. The experimental data presented here provides strong validity to theoretical models of MFH, especially the need for size-tuned, monodisperse MNPs for maximizing SLP.

The in vitro therapeutic efficacy of MFH to induce cell death has been demonstrated in heating experiments with Jurkat cells as a function of both MNP concentration and size (FIGS. 14 and 15). As expected, increasing MNP concentration increases heating rates; consequently reduction in % viability is also enhanced (FIG. 15). As described earlier, enhancing MFH by increasing MNP concentration, which is an extrinsic parameter, does not indicate an improvement in the overall therapeutic potency of MFH. The key result, however, is the significant decrease in % viability due to the optimum 16 nm sized MNPs compared to the 12 and 13 nm MNPs under the same AMF conditions. This result (FIG. 15) underscores the central idea of tailoring size for a specific frequency in order to intrinsically improve the therapeutic potency of MFH.

Systematic experiments show that magnetite MNPs, with optimal magnetic properties and tailored to a specific alternating magnetic field frequency (f=373 kHz) can show enhancement in MFH. Specifically, a peak in the heating rate or SLP as a function of MNP size has been clearly demonstrated and in vitro heating shows that optimized MNPs (16 nm) and narrow size distributions (a 30% difference in SLP is observed between σ˜0.175 and σ˜266) have maximum efficiency in reducing cell viability, suggesting our SLP data translates to cell populations. All this is achieved by synthesizing monodisperse MNPs via organic synthesis routes and successfully transferring them to aqueous phase using a biocompatible amphiphilic polymer. A characterization protocol ensures that the MNPs meet the criteria: (1) uniform shape and monodispersity, (2) phase purity, (3) stable magnetic properties approaching that of the bulk, (4) colloidal stability, (5) substantial shelf life and (6) pose no significant in vitro toxicity. This presents a way to tailor/synthesize optimal, biocompatible MNPs for MFH at any applied frequency. 

1. A composition of magnetic nanoparticles, comprising a population of magnetic nanoparticles having a narrow size distribution, wherein greater than about 70% of the magnetic nanoparticles in the population have a diameter that is less than 10.5 nanometers (nm) from the median diameter.
 2. The composition of claim 1, wherein the narrow size distribution obeys a volume weighted distribution function as measured by magnetic measurements or dynamic light scattering (DLS).
 3. The composition of claim 1, wherein the narrow size distribution obeys a number-weighted distribution function as measured by transmission electron microscopy (TEM).
 4. The composition in claim 2, wherein the narrow size distribution obeys a log normal distribution and comprises a multiplicative standard deviation of less than about 1.35.
 5. The composition of claim 2, wherein greater than about 70% of the magnetic nanoparticles in the population have a diameter that is less than 8.8 nm from the median diameter.
 6. The composition of claim 2, wherein the narrow size distribution comprises a log-normal distribution with median diameter and a multiplicative standard deviation of less than about 1.22.
 7. The composition of claim 3, wherein greater than about 70% of the magnetic nanoparticles in the population have a diameter that is less than 3 nm from the median number-weighted diameter.
 8. The composition of claim 3, wherein the narrow size distribution comprises a median diameter and a multiplicative standard deviation of less than about 1.11.
 9. The composition of claim 1, wherein the population of magnetic nanoparticles comprises a median diameter ranging from about 12 nm to about 30 nm or from about 5 nm to about 30 nm.
 10. The composition of claim 1, wherein the population of magnetic nanoparticles comprises a median hydrodynamic diameter ranging from about 30 nm to about 100 nm in aqueous solution.
 11. The composition of claim 1, wherein at least one magnetic nanoparticle of the population of magnetic nanoparticles comprises a magnetite (Fe₃O₄) core coated with a polymer.
 12. The composition of claim 11, wherein the magnetite core is a single, defect-free crystal of magnetite.
 13. The composition of claim 11, wherein the polymer is selected from the group consisting of an ethylene oxide/propylene oxide block copolymer, polyethylene oxide polymer, polyethylene glycol polymer, poly(maleic anhydride alt-1-octadecene) polymer and poly(maleic anhydride alt-1-octadecene)-polyethylene glycol polymer (PMAO-PEG).
 14. The composition of claim 1, wherein the population of magnetic nanoparticles is produced by a method comprising the steps of: combining an iron precursor and a surfactant in an organic solvent, wherein the molar ratio of surfactant to iron precursor is greater than 10:1; heating the iron precursor and the surfactant in the organic solvent to form a first population of magnetic nanoparticles; and combining the first population of magnetic nanoparticles with a polymer to form a second population of magnetic nanoparticles, wherein the magnetic nanoparticles of the second population comprise the polymer, and wherein the second population of magnetic nanoparticles has a narrow size distribution and is dispersible in an aqueous solution.
 15. A method of making a population of magnetic nanoparticles, the method comprising: combining an iron precursor and a surfactant in an organic solvent to form an iron precursor solution, wherein the molar ratio of surfactant to iron precursor is greater than 10:1; heating the iron precursor solution to form a first population of magnetic nanoparticles; and combining the first population of magnetic nanoparticles with a polymer to form a second population of magnetic nanoparticles, wherein the magnetic nanoparticles of the second population comprise the polymer, and wherein the second population of magnetic nanoparticles has a narrow size distribution and is dispersible in an aqueous solution.
 16. The method of claim 15, wherein the second population of magnetic nanoparticles has a narrower size distribution than the first population of magnetic nanoparticles.
 17. The method of claim 15, further comprising purging the iron precursor solution under an argon or nitrogen atmosphere.
 18. The method of claim 15, wherein heating the iron precursor solution comprises a gradient temperature heating phase and a stable temperature heating phase, and wherein a reaction time for a combination of the gradient temperature heating phase and the stable temperature heating phase is longer than twenty hours.
 19. The method of claim 15, wherein the iron precursor has the formula: Fe³⁺(R¹)₃, wherein R¹ is a substituted or unsubstituted saturated C₁-C₂₄ carboxylic acid or a substituted or unsubstituted unsaturated C₁-C₂₄ carboxylic acid.
 20. (canceled)
 21. The method of claim 15, wherein the surfactant is a carboxylic acid, an alkylphosphine, a substituted or unsubstituted C₁-C₂₄ alkane, a substituted or unsubstituted C₁-C₂₄ alkene, or any combination thereof. 22.-23. (canceled)
 24. The method of claim 15, wherein the molar ratio of surfactant to iron precursor is between 10:1 and 30:1.
 25. The method of claim 15, wherein the organic solvent is a substituted or unsubstituted C₁-C₂₄ alkane or a substituted or unsubstituted C₁-C₂₄ alkene.
 26. (canceled)
 27. The method of claim 15, wherein the polymer is selected from the group consisting of an ethylene oxide/propylene oxide block copolymer, polyethylene oxide polymer, polyethylene glycol polymer, poly(maleic anhydride alt-1-octadecene) polymer and poly(maleic anhydride alt-1-octadecene)-polyethylene glycol co-polymer (PMAO-PEG). 28.-31. (canceled)
 32. A method of producing magnetic nanoparticles with a tuned size distribution for magnetic particle imaging, the method comprising: selecting a diameter of a magnetic nanoparticle that produces a maximum spatial resolution and signal intensity at a frequency used in magnetic particle imaging; producing a population of magnetic nanoparticles having a median diameter of approximately the selected diameter of the magnetic nanoparticle that produces the maximum spatial resolution, wherein the population of the magnetic nanoparticles has a narrow size distribution. 